Borrowing Trouble? Student Loans, the Cost of Borrowing, and
Implications for the Effectiveness of Need-Based Grant Aid
Online Appendix: Not for Publication
A
CUNY and Federal Student Aid Programs
In this section, we provide additional information on the CUNY system and schools and the parameters of
federal student aid programs during our sample period.
A.1
CUNY
We distinguish between community colleges and four-year colleges in the CUNY system. Community colleges
include Borough of Manhattan Community College (BMCC), Bronx Community College, Hostos Community
College, Kingsborough Community College, LaGuardia Community College, and Queensborough Community
College. Four-year colleges include Baruch College, Brooklyn College, City College of New York, College
of Staten Island, Hunter College, John Jay College of Criminal Justice, Lehman College, Medgar Evers
College, New York City College of Technology (NYCCT), Queens College, and York College. However,
several of CUNY’s four-year (“senior”) colleges offer both associates’ and bachelors’ degrees (College of
Staten Island, John Jay, Medgar Evers, NYCCT, and York College). All of CUNY’s community colleges
only offer associates’ degrees.
CUNY tuition and the range of fees, estimated living expenses, and total cost of attendance faced by
full-time, full-year, in-state CUNY students during the years we examine are displayed below in Table A.1.
Cost of Attendance (COA) equals allowable living expenses include the cost of books and supplies, room
and board, transportation expenses, miscellaneous personal expenses, and dependent care, when applicable.
Estimated living expenses depend on a students’ planned housing. Within institutions, students within the
same broad category (e.g., full-time freshmen living off campus) are all classified as having the same COA,
even if actual living expenses vary substantially across individuals within a given group.
1
Table A.1: Parameters of CUNY System Institutions: 2006-07 through 2011-12
Nominal Annual Expenses
Two-year CUNY colleges Four-year CUNY colleges
Tuition, 2006-07 through 2008-09
$2,800
$4,000
Tuition, 2009-10
$3,150
$4,600
Tuition, 2010-11
$3,600
$5,130
Fees
$268 - $355
$252 - $477
Books and supplies
$879 - $1,146
$879 - $1,146
Living expenses (off campus)
$5,905 - $6,568
$5,905 - $6,568
Living expenses (with family)
$12,916 - $16,231
$12,916 - $16,231
Total cost of attendance
$9,852 - $21,332
$11,036 - $22,984
A.2
Federal Pell Grant Program
Table A.2 displays the minimum and maximum (nominal) Pell Grant awards and Pell Grant eligibility
threshold during the years we examine. The relationship between EFC and Pell Grant aid for students
eligible for an award that is greater than the minimum and less than the maximum does not vary over the
years we examine. As long as a student’s COA is greater than her statutory Pell Grant, Pell Grant aid only
depends on EFC. For most CUNY students, this constraint is not binding.
Table A.2: Parameters of the Pell Grant Program: 2006-07 through 2010-11
2006-07 2007-08 2008-09 2009-10 2010-11
Minimum Pell Grant
$400
$400
$890
$976
$555
Maximum Pell Grant
$4,050
$4,310
$4,731
$5,350
$5,550
Eligibility threshold (EFC) $3,850
$4,110
$4,041
$4,617
$5,273
Students with a zero EFC receive the maximum Pell Grant award. For the 2006-07 through 2008-09
academic years, dependent students and independent students with children would automatically receive a
$0 EFC if their family income fell below $20,000 and their parents either received means tested benefits
during the year or were eligible to file a simplified tax return (indicating low assets). In 2010, the income
limit was raised to $30,000.1
A.3
Federal Direct Loans
Prior to 2010, schools participated in one of two parallel federal lending programs: the William D. Ford
Federal Direct Loan Program and the Federal Family Education Loan (FFEL) Program, through which the
federal government guaranteed loans originated by private lenders. The 2010 Health Care and Education
Reconciliation Act abolished the FFEL program. This reform did not affect CUNY students because CUNY
schools were already participating in Direct Loan Program prior to 2010. Students pay an origination
1 See
http://www.ifap.ed.gov/eannouncements/attachments/0708EFCFormulaGuide.pdf
http://www.ifap.ed.gov/efcformulaguide/attachments/111408EFCFormulaGuide0910.pdf for further details.
2
and
fee when taking out federal loan aid, but this fee is continuous in the amount borrowed (approximately 1
percent).
Borrowing limits vary slightly over our sample period. Prior to fall 2007, first-year, dependent students
could borrow a maximum of $2,625 in subsidized federal loans. Prior to fall 2008, dependent students
were not eligible to borrow above the subsidized limit and independent students were allowed to borrow an
additional $4,000 in unsubsidized loans. Students who are considered to be in their second year for federal
loan eligibility purposes (i.e., those who have accumulated between 30 and 59 credits) with unmet need
can borrow up to $4,500 in subsidized loans ($3,500 prior to fall 2007), while students in their third year
and above (i.e., those who have accumulated at least 60 credits) who have unmet need can borrow up to
$5,500. Regardless of credits accumulated, students in two-year degree programs are never considered to
be third year students for federal borrowing purposes. The overall borrowing limits dependent students
face are $6,500 in their second year and $7,500 as upper years ($3,500 and $5,500, respectively, prior to
fall 2008), while independent students can borrow up to $10,500 in their second year and $12,500 in their
third year and beyond ($7,500 and $10,500, respectively, prior to fall 2008). Students are limited in the
total amount of federal debt they can incur during their undergraduate education. Dependent students
can borrow up to $31,000 overall ($23,000 subsidized) and independent students can borrow up to $57,500
($23,000 subsidized). See studentaid.ed.gov/types/loans for additional details.
An individual student’s subsidized loan eligibility may be less than the amounts described above. According to the Department of Education’s Federal Student Aid Handbook, a school cannot package a subsidized
loan that exceeds a student’s unmet need, which is equal to the cost of attendance minus EFC and other
financial assistance (grants and work-study). Unsubsidized loans eligibility is limited to be no more than the
total cost of attendance minus other financial assistance and subsidized loans (e.g., unsubsidized loans can
be used to replace EFC). This latter constraint is rarely binding.
3
Appendix B: Additional Figures and Tables
Figure B.1: Sample CUNY Financial Aid Award Letter
4
Figure B.2: Sample CUNY Loan Application Form
Aca d em ic Y ea r:
2013-2014
Summer 2013
Fall 2013
Spring 2014
City University of New York
695 Park Avenue; New York, NY 10065
Office of Financial Aid
Room 241 North
Tele.: 212-772-4820
WILLIAM D. FORD FEDERAL DIRECT STAFFORD LOAN APPLICATION
(Please print clearly in BLACK or BLUE ink)
*Incomplete applications will not be processed*
Student’s Information:
Last Name: ____________________________________________ First Name: _________________________________________ Middle Initial: ________
SS#: _______________ /________________/__________________
Date of Birth: _______________ /________________/__________________
Permanent Address: (*P.O. boxes or dorm addresses CANNOT be used as a permanent address)
Street: _________________________________________________________________________________ Apt#: ________________
City, State: _____________________________________________________________________________ Zip Code: _______________
Mailing Address, if different from permanent address:
Street: _________________________________________________________________________________ Apt#: ________________
City, State: _____________________________________________________________________________ Zip Code: _______________
Phone #: (______________)______________________________
Hunter E-mail Address: ___________________________ @hunter.cuny.edu
All loans will be disbursed in two (2) equal payments, Fall 2013 and Spring 2014. If the student is eligible for a Summer 2013 loan and he/she
indicates that they would like to be considered for a Summer disbursement, the loan will be disbursed in three (3) payments, instead of two.
**One (1) semester loans will only be processed for graduating students.
I am registered for at least 6 credits during the Summer 2013 semester.
Yes
No
If yes: I would like to be considered for a Summer loan disbursement.
Yes
No
I am graduating at the end of the following semester:
**Undergraduates Only: I would like this loan for Summer 2013
only, because I am anticipating Financial Aid for Fall 2013 &
Spring 2014.
Yes
No
Summer 2013
Fall 2013
Spring 2014
I am not graduating during the 2013 – 2014 academic year
Total loan amount requested for the 2013-2014 academic year:
You must round the amount to the nearest whole dollar.
Undergraduates:
I understand that I will be considered for a SUBSIDIZED loan first.
Yes
If I am not eligible for a subsidized loan, I authorize the Office of
Financial Aid to process an UNSUBSIDIZED loan.
Yes
No
.00
$
Graduates:
I understand that Graduate students are no longer eligible for
subsidized loans. I authorize the Office of Financial Aid to process an
UNSUBSIDIZED loan.
Yes
**UNDERGRADUATE STUDENTS: Will you be pursuing your first Bachelor’s degree during the 2013-14 academic year?
Yes
No
Borrower’s Certification: My signature below certifies that I am aware I must be making Satisfactory Academic Progress in order to receive the Federal Direct Stafford
Loan(s) I am applying for. I must complete and sign a Master Promissory Note, if I am required to do so. I also understand that if I have not completed the required
steps listed on theright of this application, my loan will not be processed. I understand that it is my responsibility to follow up on the status of my loan application if I
do not receive notification. I am also aware that my attendance must be verified by the Office of Financial Aid, before a disbursement is made in accordance with the
Financial Aid ‘Schedule of Payments’.
A p p l i c a n t ’ s s i g n a t u r e : _______________________________________________________
OFFICE USE ONLY
UG
G
SSW
U
F
S
Undergraduate Annual Loan Limits and Rates
Crds
Completed
0 – 29.9
Dependent
Independent
$5,500 (Max. Subsidized= $3,500)
$9,500 (Max. Subsidized= $3,500)
30 – 59.9
$6,500 (Max. Subsidized= $4,500)
$10,500 (Max. Subsidized= $4,500)
60+
$7,500 (Max. Subsidized= $5,500)
$12,500 (Max. Subsidized= $5,500)
S u b s i d i z e d interest rate: 6.8% fixed (disbursed on or after July 1st, 2013
and prior to July 1st, 2014)
Unsubsidized interest rate: 6.8% fixed (disbursed on or after July 1st, 2006)
D a t e : _______________________
Graduate Annual Loan Limits and Rates
$20, 500
U n s u b s i d i z e d interest rate: 6.8% fixed (disbursed on
or after July 1st, 2006)
**Effective for loan disbursements beginning on or after
July 1st, 2012, graduate and professional students are
no longer eligible to receive Direct Subsidized Loans.
Direct Subsidized Loans disbursed prior to the 20122013 academic year are not affected by this change.
Notes: Available at http://www.hunter.cuny.edu/onestop/finances/financial-aid/.
5
REQUIREMENTS:
The following 4 criteria are R E Q U I R E D in order for the
Office of Financial Aid to process your loan within 15
business days. When your application is reviewed and the
4 criteria have not been completed, your application will
not be processed. The Office of Financial Aid will NOT
return any incomplete applications. Check with the Office
of Financial Aid after 15 business days to follow up on
your application status.
Have a valid 2013-2014 FAFSA Application
(www.FAFSA.ED.GOV)
Must be a matriculated student, registered for
at least 6 credits, within your grade level, per
semester during the 2013-2014 academic
year
Complete an ‘Entrance Counseling’ quiz**
(www.STUDENTLOANS.GOV)
* You must attach the confirmation page
Complete a Master Promissory Note (MPN) **
(www.STUDENTLOANS.GOV)
**Your loan request will be applied to your CUNYfirst
account within 15 business days or less.
LOAN ELIGIBILITY DETERMINATION:
The approved loan amount will be determined by CUNY’s
Cost of Attendance (COA), minus the Expected Family
Contribution (EFC), which is determined by your FAFSA
application for 2013-2014. Any financial aid and
scholarships you are awarded will be deducted from your
COA.
NOTIFICATION:
Once your loan is processed you should receive an award
notification, by mail, from CUNY’s University Application
Processing Center. If there are any discrepancies on your
award notification, you must contact the Office of Financial
Aid immediately. Once a disbursement has occurred, you
will receive a disclosure statement from the loan servicing
agency.
R E FUND :
Check Hunter College’s ‘Schedule of Payments’ for loan
disbursement dates. Refunds are mailed by check or you
can sign up for Direct Deposit, visit
www.hunter.cuny.edu/finaid to print the form. D i r e c t
D e p o s i t i s s t r o n g l y e n c o u r a g e d because you will get
your funds on the same day of disbursement. If your check
is mailed, you will get it 3 or 5 days later depending on your
local post office. If checks are lost via mail it will take
about 4 weeks or longer for you to get a replacement
check.
* * N o t e t o T r a n s f e r S t u d e n t s : Your 2013-2014 annual
loan limit may be affected if you borrowed loans at another
institution for Summer 2013 and/or Fall 2013.
2500
2000
1500
0
500
1000
Pell Grant Aid
3000
3500
4000
Figure B.3: The Empirical Distribution of Pell Grant Aid by Distance to Eligibility Threshold: Returning
Students
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
Distance to Pell Grant Eligibility Threshold
Notes: Second- and third-year CUNY undergraduate degree-seeking students; 2005 through 2010 cohorts. $200 EFC bins. Each
circle represents the average Pell Grant aid received by students in the bin. Larger circles represent a larger underlying sample
size. All dollar amounts adjusted to represent constant 2012$.
2000
1500
1000
0
500
Number of Students
2500
3000
Figure B.4: The Density of EFC at the Pell Grant Eligibility Threshold: Returning Students
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
Distance to Pell Grant Eligibility Threshold
Notes: Second- and third-year CUNY undergraduate degree-seeking students; 2005 through 2010 cohorts. $200 EFC bins. Each
circle represents the total number of students in the bin. All dollar amounts adjusted to represent constant 2012$.
6
900
600
0
300
Total Federal Loan Aid
1200
1500
Figure B.5: The Reduced Form Impact of Pell Grant Eligibility and Generosity on Total Borrowing: Returning Students
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
Distance to Pell Grant Eligibility Threshold
Notes: Second- and third-year CUNY undergraduate degree-seeking students; 2005 through 2010 cohorts. $200 EFC bins. Each
circle represents average loan aid (subsidized + unsubsidized Federal Direct Loans) received by students in a given bin. Larger
circles represent a larger underlying sample size. All dollar amounts adjusted to represent constant 2012$.
Figure B.6: Impacts on Overall Borrowing Driven by a Reduction in Subsidized Borrowing
400
300
200
Unubsidized Federal Loan Aid
100
700
600
500
400
300
200
0
0
100
Subsidized Federal Loan Aid
800
500
B. Unsubsidized Loans
900
A. Subsidized Loans
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
-4000
Distance to Pell Grant Eligibility Threshold
-3000
-2000
-1000
0
1000
2000
3000
4000
Distance to Pell Grant Eligibility Threshold
Notes: First-year CUNY undergraduate degree-seeking students; 2007 through 2011 cohorts. $200 EFC bins. Each circle
represents average subsidized (A) or unsubsidized (B) Federal Direct Loan aid received by students in the bin. Larger circles
represent a larger underlying sample size. All dollar amounts adjusted to represent constant 2012$.
7
Figure B.7: Reduced Form Impacts of Pell Grant Aid on Educational Outcomes
A. Reenrollment
27
26
25
Cumulative Credits Attempted
23
-3000
-2000
-1000
0
1000
2000
3000
4000
-4000
-3000
-2000
-1000
0
1000
2000
Distance to Pell Grant Eligibility Threshold
Distance to Pell Grant Eligibility Threshold
C. Cumulative Credits Earned
D. GPA
3000
4000
3000
4000
14
2.3
15
2.4
16
2.5
17
GPA
2.6
18
2.7
19
20
2.8
-4000
Cumulative Credits Earned
24
.85
.8
.75
.7
.65
Probability of Enrollment in Following Year
.9
28
B. Credits Attempted
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
-4000
Distance to Pell Grant Eligibility Threshold
-3000
-2000
-1000
0
1000
2000
Distance to Pell Grant Eligibility Threshold
Notes: First-year CUNY undergraduate degree-seeking students; 2007 through 2011 cohorts. $200 EFC bins. Each circle
represents the average probability of enrolling in the following year (A), average credits attempted including credit equivalents
from remedial courses (B), average credits earned (C), and average GPA (D) among currently enrolled students. Larger circles
represent a larger underlying sample size.
8
0.6
0.4
0.2
Probability
0.8
1.0
Cumulative
Distribution FunctionCumulative
of Loans, 1st−Year
Students
Figure B.8: Actual
and Counterfactual
Distribution
of Loans
0.0
Observed
Predicted w/ Fixed Cost
Predicted w/o Fixed Cost
0
500
1000
1500
2000
2500
3000
3500
Loans
Notes: First-year CUNY undergraduate degree seeking students subject to the exogenous subsidized loan limit; 2007 through
2011 cohorts. $500 EFC bins. The solid black line indicates the share of students with loan debt at or below the indicated level.
Red plus markers represent predictions from the maximum likelihood model. Green X markers represent predicted borrowing
predictions with no fixed cost of borrowing. All dollar amounts adjusted to represent constant 2012$.
Cumulative Distribution of Borrowing Thresholds
1.0
Figure B.9: Cumulative Distribution of Borrowing Thresholds
Year 1
Year 2
Year 3
0.6
●
0.4
Cumulative Distribution
0.8
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
0.2
●
●
●
●
●
●
Maximum
Subsidized
Loan Limit
in Sample
●
●
●
●
●
●
0.0
●
●
0
1000
2000
3000
4000
5000
Total Loans ($)
Notes: Estimated distribution of borrowing thresholds (below which observed borrowing is set to zero). See Section 7 of the
main text for model and estimation details.
9
Figure B.10: Reduced Form Impacts of Pell Grant Aid on Borrowing: NPSAS Sample
B. The Probability of Borrowing
.6
.4
0
0
500
.2
1000
1500
2000
2500
Total Loans
Probability of Borrowing
3000
.8
3500
1
4000
A. Total Borrowing
-4000
-3000
-2000
-1000
0
1000
2000
Distance from Pell Grant Eligibility Threshold
3000
4000
-4000
-3000
-2000
-1000
0
1000
2000
3000
4000
Distance from Pell Grant Eligibility Threshold
Notes: First-year undergraduate degree-seeking students attending public two- and four-year schools in 2008 National Postsecondary Student Aid Studies (NPSAS). $200 EFC bins. Each circle represents the average federal loans (Panel A) or probability
of borrowing (Panel B) among students in the bin. All dollar amounts adjusted to represent constant 2012$.
10
Table B.1: The Relationship between Pell Grant Eligibility and Predetermined Characteristics
(1) White
(2) Female
(3) Dependent (4) Immigrant
(5) Age
(6) AGI
(7) College Ed
Parent(s)
-0.002
(0.009)
-0.00005
(0.00005)
-0.004
(0.012)
-0.000001
(0.000005)
0.002
(0.006)
0.000007
(0.000002)**
0.035
(0.031)
-0.00005
(0.0001)
-0.012
(0.112)
-0.0001
(0.0001)
-1150
(553)*
-1.06
(0.78)
-0.010
(0.011)
0.000001
(0.000004)
0.517
0.864
0.014
0.490
0.755
0.019
0.639
1
1
1
4
2
2
1
38,100
38,100
38,100
38,100
38,100
38,100
35,011
-0.004
(0.010)
-0.000003
(0.000004)
0.013
(0.010)
0.00001
(0.000004)
-0.009
(0.006)
0.000004
(0.000003)
0.024
(0.017)
-0.000003
(0.00002)
0.015
(0.073)
-0.00005
(0.00003)
-1561
(658)*
-0.78
(1.58)
-0.002
(0.028)
0.00004
(0.0001)
0.669
0.101
0.202
0.368
0.340
0.048
0.889
1
1
1
2
1
3
4
46,744
46,744
46,744
46,744
46,744
46,744
43,347
A. First-year students
Pell Grant eligible
× Distance from threshold
Test of joint sig: p- value
Polynomial degree
Observations
11
B. Returning students
Pell Grant eligible
× Distance from threshold
Test of joint sig: p- value
Polynomial degree
Observations
Notes: First-, second-, and third-year CUNY undergraduate degree-seeking students; 2005 through 2011 cohorts. Observations missing information on parental education are
excluded from the Column 7 sample. Each column within a panel represents estimates from a separate regression. Clustered standard errors (institution by year) in parentheses;
** p<0.01, * p<0.05, + p<0.1. All regressions also include controls for degree program (AA versus BA), school by year fixed effects, years since entry fixed effects, and a
gC it = EF Cit − ef c0t , where ef c0t is the threshold for Pell Grant eligibility in year t), allowed to vary on either side
polynomial in student expected family contribution (EF
of the eligibility threshold. The degree of polynomial is chosen to minimize the AIC. Students with EFC greater than $4,000 from Pell Grant eligibility threshold are excluded.
All dollar amounts adjusted to represent constant 2012$.
Table B.2: The Impact of Pell Grant Aid on Subsidized and Unsubsidized Borrowing
Subsidized Loans
Unsubsidized Loans
(1) First-Year
Students
(2) Returning
Students
(3) First-Year
Students
(4) Returning
Students
-164.56
(42.03)**
-209.01
(45.45)**
-59.90
(22.96)*
-64.98
(21.39)**
0.235
(0.054)**
0.259
(0.054)**
0.059
(0.032)+
0.076
(0.033)*
38,100
46,744
38,100
46,744
Pell Grant aid
-0.333
(0.066)**
-0.392
(0.071)**
-0.094
(0.041)*
-0.116
(0.042)**
Observations
38,100
46,744
38,100
46,744
A. OLS Estimates
Pell Grant eligible
× Distance from threshold
Observations
B. 2SLS Estimates
Notes: The sample in Columns 1 and 3 includes first-year CUNY undergraduate degree-seeking students; 2007 through 2011
cohorts. The sample in Columns 2 and 4 includes second-, and third-year CUNY undergraduate degree-seeking students; 2005
through 2011 cohorts. Each column within a panel contains estimates from a separate regression. Clustered standard errors
(institution by year) in parentheses; ** p<0.01, * p<0.05, + p<0.1. All regressions also include controls for age, family AGI,
and indicators for race (white versus nonwhite), dependency status (dependent versus independent), parents’ highest level of
education (college, high school, or less than high school), level of attendance (for federal loan eligibility purposes), degree
program (AA versus BA), school by year fixed effects, years since entry fixed effects, and a quadratic in student expected family
gC it = EF Cit −ef c0t , where ef c0t is the threshold for Pell Grant eligibility in year t), allowed to vary on either
contribution (EF
gC it < 0] and EF
gC it × 1[EF
gC it < 0]. Students with
side of the eligibility threshold. Excluded instruments in Panel B are 1[EF
EFC greater than $4,000 from Pell Grant eligibility threshold are excluded. All dollar amounts adjusted to represent constant
2012$.
Table B.3: The Impact of Pell Grant Aid on Cumulative Financial Aid Received Three Years After Entry
(1) Cumulative
Pell Grant aid
(2) Cumulative
loans aid
(3) Cumulative
subsidized loans
(4) Cumulative
unsub. loans
1.189
(0.128)**
-0.574
(0.226)*
-0.402
(0.149)**
-0.173
(0.109)
Mean
$4,310
$1,004
$707
$297
Observations
32,271
32,271
32,271
32,271
First year Pell Grant aid
Notes: First-year CUNY undergraduate degree-seeking students; 2007 through 2011 cohorts. Each column contains estimates
from a separate regression. The dependent variable is cumulative financial aid in the specified category received during a
students’ first three years (not conditioned on enrollment in years 2 and 3). Clustered standard errors (institution by year) in
parentheses; ** p<0.01, * p<0.05, + p<0.1. See Table B.2 notes for a list of additional controls and excluded instruments.
Students with EFC greater than $4,000 from Pell Grant eligibility threshold are excluded. All dollar amounts adjusted to
represent constant 2012$.
12
Table B.4: The Impact of Pell Grant Aid on Other Sources of Grant Aid
(1) First-year
students
(2) Returning
students
A. Impacts on TAP Grant Aid
Pell Grant Aid
0.051
(0.046)
0.044
(0.048)
Observations
38,100
46,744
B. Impacts on Other Grant Aid
Pell Grant Aid
0.084
(0.034)*
-0.013
(0.050)
Observations
38,100
46,744
Notes: 2SLS estimates of the impact of Pell Grant aid on other grant aid. Column 1 sample includes first-year CUNY
undergraduate degree-seeking students; 2007 through 2011 cohorts. Column 2 sample includes second-, and third-year CUNY
undergraduate degree-seeking students; 2005 through 2011 cohorts. Each column within a panel contains estimates from a
separate regression. Panel A dependent variable is New York State Tuition Assistance Program (TAP) Grant aid. Panel B
dependent variable is total grant aid less TAP and Pell Grant aid. Clustered standard errors (institution by year) in parentheses;
** p<0.01, * p<0.05, + p<0.1. See Table B.2 notes for a list of additional controls and excluded instruments. Students with
EFC greater than $4,000 from Pell Grant eligibility threshold are excluded. All dollar amounts adjusted to represent constant
2012$.
13
Table B.5: The Impact of Pell Grant Aid on Borrowing:
Robustness to Varying Bandwidths and Polynomials
$3,000
$2,000
$1,000
-0.134
(0.023)**
-0.187
(0.037)**
-0.320
(0.057)**
-0.665
(0.142)**
[0.000]
[0.000]
[0.038]
[0.601]
-0.428
(0.092)**
-0.557
(0.109)**
-0.706
(0.169)**
-0.684
(0.247)**
[0.116]
[0.867]
[0.875]
[0.779]
-0.599
(0.148)**
-0.814
(0.209)**
-0.795
(0.243)**
-0.771
(0.327)*
[0.442]
[0.682]
[0.959]
[0.778]
-0.910
(0.231)**
-0.748
(0.254)**
-0.773
(0.294)**
-1.110
(0.392)**
[0.930]
[0.987]
[0.992]
[0.999]
Optimal Order
2
1
1
2
Observations
38,100
25,613
15,645
7,523
Bandwidth:
$4,000
Polynomial of order:
One
Two
Three
Four
Notes: First-year CUNY undergraduate degree-seeking students; 2007 through 2011 cohorts. Each cell represents a separate
regression. Standard errors clustered at institution level in parentheses; ** p<0.01, * p<0.05, + p<0.1. All regressions
include controls for age, family AGI, and indicators for race (white versus nonwhite), dependency status (dependent versus
independent), parents’ highest level of education (college, high school, or less than high school), level of attendance (for federal
loan eligibility purposes), degree program (AA versus BA), school by year fixed effects, and a polynomial in student expected
gC it = EF Cit − ef c0t , where ef c0t is the threshold for Pell Grant eligibility in year t), allowed to vary
family contribution (EF
on either side of the eligibility threshold. Degree of polynomial is indicated in the first column. Optimal order of polynomial
chosen using Akaike Information Criterion. Square brackets include p-values from test of joint significance of $200 EFC bin
gC it < 0] and EF
gC it × 1[EF
gC it < 0]. Students
dummies included as additional regressors. Excluded instruments are 1[EF
with EFC greater than the indicated distance from Pell Grant eligibility threshold are excluded. All dollar amounts adjusted
to represent constant 2012$.
14
Table B.6: The Impact of Pell Grant Aid on Borrowing: Estimates from Local Linear Regressions
OLS
(1) FS
2SLS
(2) RF
(3) RD
(4) RK
(5) RD/RK
-0.759
(0.142)**
-3.112
(0.479)**
-0.275
(0.058)**
-1.486
(0.259)**
-0.321
(0.058)**
-1.332
(0.178)**
<0.001
0.030
0.031
A. Imbens-Kalyanaraman Optimal Bandwidth
Pell Grant eligible
× Distance from threshold
378.10
(26.520**
-277.63
(52.28)**
-0.798
(0.014)**
0.223
(0.047)**
Pell Grant aid
Crowd-out | borrower
H0: crowd-out >-1, p- value
Bandwidth
1,639
2,078
2,078
2,078
2,078
Observations
12,519
16,360
16,360
16,360
16,360
-0.657
(0.149)**
-2.704
(0.538)**
-0.429
(0.114)**
-2.223
(0.469)**
-0.492
(0.101)**
-2.025
(0.282)**
<0.001
0.005
<0.001
B. Fan-Gijbels Rule of Thumb Bandwidth
Pell Grant eligible
× Distance from threshold
379.20
(25.52)**
-253.63
(58.60)**
-0.767
(0.013)**
0.336
(0.091)**
Pell Grant aid
Crowd-out | borrower
H0: crowd-out >-1, p- value
Bandwidth
1,774
1,358
1,358
1,358
1,358
Observations
13,726
13,217
13,217
13,217
13,217
-0.720
(0.146)**
-3.000
(0.512)**
-0.281
(0.065)**
-1.503
(0.299)**
-0.330
(0.065)**
-1.375
(0.207)**
<0.001
0.047
0.035
C. Ludwig-Miller Cross Validation Bandwidth
Pell Grant eligible
× Distance from threshold
451.50
(28.96)**
-265.10
(53.44)**
-0.329
(0.122)**
0.229
(0.053)**
Pell Grant aid
Crowd-out | borrower
H0: crowd-out >-1, p- value
Bandwidth
Observations
283
1,942
1,942
1,942
1,942
2,046
15,150
15,150
15,150
15,150
Notes: Estimates from local linear regressions of Pell Grant aid and loan aid on Pell Grant eligibility and generosity (OLS
estimates) and loan aid on Pell Grant aid (2SLS estimates) using a uniform kernel. First-year CUNY undergraduate degreeseeking students; 2007 through 2011 cohorts. Each column within a panel represents a separate regression. Standard errors
clustered at institution by year level in parentheses; ** p<0.01, * p<0.05, + p<0.1. See main text for description of bandwidth
selection procedures.
15
Table B.7: Heterogeneity in the Impact of Pell Grant Aid on Borrowing: Returning Students
Student has characteristic:
(1) Immigrant
(2) Dependent
Student
N
N
Y
-0.240
(0.465)
-0.522
(0.098)**
Y
(3) College Educated
Parent
N
Y
(4) Attending
Community College
N
Y
A. Dependent Var = Total Loans
Pell Grant Aid
-0.584
-0.420
(0.145)** (0.131)**
Test of eq: p- value
Crowd-out | borrower
0.413
-1.922
-1.806
Test of eq: p- value
Observations
0.005
-0.593
-0.250
(0.116)** (0.135)+
0.901
0.055
0.561
(0.359)** (0.436)**
H0: crowd-out > -1, p -value
-0.496
-0.471
(0.164)** (0.122)**
0.032
-0.869
-1.973
(1.479)
(0.268)**
--
<0.001
-1.937
-1.694
(0.505)** (0.360)**
0.032
0.027
-2.136
-1.062
(0.272)** (0.594)+
<0.001
0.458
0.951
0.806
0.890
0.597
46,744
46,744
43,347
46,744
16
B. Dependent Var = Credits Earned
Pell Grant Aid ($1k)
Test of eq: p- value
Observations
0.052
(0.556)
0.863
(0.527)
2.021
(1.298)
0.379
(0.376)
0.071
(0.562)
0.848
(0.476)+
0.153
(0.395)
1.420
(0.853)+
0.303
0.211
0.263
0.178
46,744
46,744
43,347
46,744
Notes: 2SLS estimates of the impact of an additional dollar of Pell Grant aid on borrowing for all students and borrowing among students who would have borrowed in the
absence of the increase in Pell Grant aid (Panel A) or credits earned during academic year (Panel B). Second- and third-year CUNY undergraduate degree-seeking students;
2005 through 2011 entry cohorts. Each column within a panel represents estimates from a separate regression. Clustered standard errors (institution by year) in parentheses;
** p<0.01, * p<0.05, + p<0.1. See Table B.2 notes for a list of additional controls. All covariates are fully interacted with indicator for whether a student is a first- or
second-generation immigrant (Column 1 specification), is a dependent student (Column 2 specification), has a college educated parent (Column 3 specification), or is attending
gC it < 0] and EF
gC it × 1[EF
gC it < 0] interacted with indicator for having the listed characteristic.
a community college (Column 4 specification). Excluded instruments are 1[EF
Students with EFC greater than $4,000 from Pell Grant eligibility threshold are excluded. All dollar amounts adjusted to represent constant 2012$.
Table B.8: Heterogeneity in the Impacts of Pell Grant Aid by TAP Grant receipt and Minimum Pell Grant:
First-Year Students
1. Any TAP Grant
2. High Minimum Pell
N
Y
N
Y
-0.775
(0.274)**
-0.352
(0.087)**
-0.470
(0.115)**
-0.419
(0.134)**
A. Dependent Var = Total Loans
Pell Grant Aid
Test of eq: p- value
Crowd-out | borrower
H0: crowd-out > -1, p -value
0.138
0.77
-3.008
-1.571
-2.093
-1.683
(0.813)**
(0.274)**
(0.358)**
(0.410)**
0.007
0.018
0.001
0.048
Test of eq: p- value
Observations
0.596
0.828
38,100
38,100
B. Dependent Var = Credits Earned
Pell Grant Aid ($1k)
Test of eq: p- value
Observations
-0.766
(0.886)
0.208
(0.428)
0.534
(0.611)
-0.162
(0.498)
0.279
0.377
38,100
38,100
Notes: 2SLS estimates of the impact of an additional dollar of Pell Grant aid on borrowing for all students and borrowing
among students who would have borrowed in the absence of the increase in Pell Grant aid (Panel A) or credits earned during
academic year (Panel B). First-year CUNY undergraduate degree-seeking students; 2007 through 2011 cohorts. Each column
within a represents a separate regression. Clustered standard errors (institution by year) in parentheses; ** p<0.01, * p<0.05,
+ p<0.1. High minimum Pell years are 2009 and 2010. See Table B.2 notes for a list of additional controls. All covariates are
fully interacted with indicator for any TAP Grant received (column 1 specification) or high minimum Pell Grant (column 2
gC it < 0] and EF
gC it × 1[EF
gC it < 0] . Students with EFC greater than $4,000
specification). Excluded instruments are 1[EF
from Pell Grant eligibility threshold in their first year are excluded. All dollar amounts adjusted to represent constant 2012$.
17
Table B.9: Characteristics of Switchers
Gender
Female
Male
Race
Black
Hispanic
White
Other
Dependency status
Dependent
Independent
Parental education
Less than high school
High school
Some college +
Missing
Initial degree program
AA/AS
BA/BS
Foreign born
Parent
Student
SAT scores
Missing
Above median math
Below median math
Above median verbal
Below median verbal
β =
E[X|switcher]
E[X]
H0: β =1
(p- value)
E[X]
E[X|switcher]
0.54
0.46
0.66
0.35
1.22
0.75
0.489
0.500
0.32
0.29
0.25
0.14
0.46
0.44
0.03
0.10
1.43
1.53
0.13
0.73
0.404
0.340
0.168
0.692
0.92
0.08
0.98
0.02
1.07
0.23
0.526
0.544
0.05
0.39
0.49
0.08
0.10
0.39
0.45
0.06
1.94
0.99
0.91
0.72
0.496
0.986
0.789
0.808
0.40
0.60
0.34
0.75
0.85
1.25
0.703
0.384
0.51
0.18
0.50
0.16
0.98
0.91
0.962
0.892
0.32
0.20
0.48
0.19
0.49
0.55
0.18
0.31
0.05
0.45
1.72
0.91
0.65
0.24
0.91
0.189
0.884
0.347
0.268
0.787
Notes: First-year CUNY undergraduate degree-seeking students; 2007 through 2011 cohorts. E [X] represents the average
characteristic among students near the Pell Grant eligibility threshold, estimated via a regression of that characteristic on
gC (allowed to vary on either side of the eligibility threshold). β = E[X|switcher] represents the relative
a quadratic in EF
E[X]
likelihood that an individual with characteristic X is a switcher. We estimate this term by taking the ratio of the coefficient on
gC it < 0] and a quadratic in EF
gC (allowed to vary on either side of the
gC it < 0] from a regression of any borrowing 1[EF
1[EF
eligibility threshold) using the full sample to the same coefficient when the sample is limited to students who have characteristic
X. E [X|Switcher] = βE [X]. The fourth column displays the p − value from the test of β = 1, which is a test of whether the
probability that a switcher has characteristic X significantly differs from the probability that a member of the full sample has
characteristic X. Students with EFC greater than $4,000 from Pell Grant eligibility threshold in their first year are excluded.
All dollar amounts adjusted to represent constant 2012$.
18
Table B.10: Heterogeneity in the Impact of Pell Grant Aid on Borrowing
by Availability of Online Loan Application
(1) First-year students
Online loan application?
Pell Grant aid
N
Y
N
Y
-0.417
(0.110)**
-0.452
(0.166)**
-0.416
(0.116)**
-0.684
(0.162)**
Test of eq: p- value
Crowd-out | borrower
H0: crowd-out > -1, p -value
Test of eq: p- value
Observations
(2) Returning students
0.179
0.859
-1.870
(0.348)**
-1.720
(0.480)**
-1.705
(0.410)**
-2.158
(0.290)**
0.006
0.067
0.043
<0.001
0.936
0.804
38,100
46,744
Notes: 2SLS estimates of the impact of an additional dollar of Pell Grant aid on borrowing for all students and for would-be
borrowers. Column 1 sample includes first-year CUNY undergraduate degree-seeking students; 2007 through 2011 cohorts.
Column 2 sample includes second- and third-year CUNY undergraduate degree-seeking students; 2005 through 2011 cohorts.
Each column represents estimates from a separate regression. Clustered standard errors (institution by year) in parentheses; **
p<0.01, * p<0.05, + p<0.1. See Table B.2 notes for a list of additional controls. All covariates are fully interacted with indicator
for whether a student is attending a school that provides an online application for loans. Four of the 17 CUNY institutions
gC it < 0] and EF
gC it × 1[EF
gC it < 0] interacted with
provided an online loan application. Excluded instruments are 1[EF
indicator for having the listed characteristic. Students with EFC greater than $4,000 from Pell Grant eligibility threshold are
excluded. All dollar amounts adjusted to represent constant 2012$.
19
Appendix C: Proofs
In this appendix we demonstrate that the solution has the form described in Section 3. Proofs of the
predictions in Section 3.1 follow directly.
First, the student’s problem has between one and two optima. The strict concavity of u (·) and w (·)
and convexity of C (·), along with piecewise linearity of the cost of borrowing and the regularity condition
w00 (s) ≤ −Rm Ct00 (s), imply that the problem is strictly concave in both d and s where differentiable. The
proof is trivial except to note that the regularity condition is sufficient because
∂2
∂2
u (c1 ) = 2 u w (s) − Rs d − κs (Rm − Rs ) d − d¯ − ξ Ct (s) − g − EF C − d¯
2
∂s
∂s
=
∂
(w0 (s) + κs ξ (Rm − Rs ) Ct0 (s)) u0 (c1 )
∂s
2
= (w00 (s) + κs ξ (Rm − Rs ) Ct00 (s)) u0 (c1 ) + (w0 (s) + κs ξ (Rm − Rs ) Ct0 (s)) u00 (c1 )
and
w00 (s) ≤ −Rm Ct00 (s) ⇒ w00 (s) + κs ξ (Rm − Rs ) Ct00 (s) ≤ 0 ⇒
∂2
u (c1 ) < 0
∂s2
Therefore, the problem is concave except for the discontinuity at d = 0. The domain of s is bounded
by assumption, which therefore places bounds on d because consumption cannot be negative. Hence, there
is at least one solution. The solution will not include d at the lower bound that makes c0 = 0 because
c1 > 0 = c0 ⇒
∂u(0)
∂d
≥
∂u(c1 )
∂d
≥
∂βu(c1 )
,
∂d
which implies that total utility would be increased by raising d
above this level. Similarly, s is bounded from above by non-negativity of c0 and the fact that d is bounded
¯ and the upper bound for s will not be optimal. Any solution for observed students (for whom
above by d,
the lower bound s = 0 is revealed to be suboptimal) satisfies the first order condition with respect to s (1),
and either the first order condition with respect to d given by equation (2), d = 0, or d = d¯ (3).
Second, the solution is unique with probability one. Because the entire problem would be concave if not
for the discontinuity, and because the discontinuity reduces utility for values of d greater than zero, any
solution with d < 0 is unique. It may be, however, that an allocation with d > 0 gives the same utility as
one with d = 0. If two solutions exist for a given level of EFC we denote the positive debt amount chosen
in one solution by d. Because student resources are continuously distributed, d is optimal with probability
zero.
Third, the solution takes the monotonically ranked form described in Section 3. The empirical size
(possibly zero) of each group will depend on the parameter values and the distribution of resources among
20
students. Here we establish the theoretical existence of each group of students and their ranking by resources.
Consider schooling level s̄ satisfying the equation Rs C 0 (s̄) = w0 (s̄) and ω = u−1 (Rs βu (w (s̄) + )) +
C (s̄) − EF C − g for some > 0.
If debt is zero, this allocation gives u (c0 ) = Rs βu (w (s̄) + ) >
Rs βu (w (s̄)) = u (c1 ). Raising s would increase total utility, but lowering d by an amount that causes
the same reduction in c0 would cause a greater rise in c1 , implying that a negative value of debt must be
optimal.
Since d∗ < 0, κ0 = κs = λ = 0. (1) and (2) hold, and combining them gives Rs C 0 (s∗ ) = w0 (s∗ ).
while differentiation of (2) gives
∗
∂d
∂g
∂s∗
∂g
= 0,
00
u (c0 )
= − u00 (c0 )+R
2 βu00 (c ) ∈ (−1, 0). Note that g and ω are interchangeable
1
s
in the problem, the optimal allocation responds to ω in the same way that it responds to g: Higher values
of ω reduce d∗ and have no effect on s∗ . The conditions hold until ω becomes low enough that d∗ = 0. We
label those with resources high enough to induce negative borrowing (i.e. net saving) Group A.
At d∗ = 0,
∂d∗
∂g
= 0 and of the first-order conditions only (2) holds. We label the mass of students with
exactly zero debt as Group B. Differentiation gives
∂s∗
C 0 (s∗ ) u00 (c0 )
=−
>0
2
2
∂g
C 00 (s∗ ) u0 (c0 ) − C 0 (s∗ ) u00 (c0 ) − w00 (s∗ ) u0 (c0 ) − w0 (s∗ ) u00 (c0 )
Denote the optimal schooling choice when d∗ = 0 as s∗0 (suppressing the arguments of this function to simplify
notation). If the fixed cost of borrowing is not too large there will be additional groups with positive debt.
Students in Group B obtain utility u (ω + EF C + g − C (s∗0 )) + βu (w (s∗0 )). Students with positive debt ob
tain utility u (ω + EF C + g − C (s∗ ) − γ)+βu w (s) − Rs d − κs (Rm − Rs ) d − d¯ − ξ Ct (s∗ ) − g − EF C − d¯ .
The level of debt for which the two utilities are equivalent is d. If d < d¯ there will be a Group C
∗
for which d ∈ d, d¯ and both (1) and (2) hold. As with Group A, Rs C 0 (s∗ ) = w0 (s∗ ), ∂s
∂g = 0, and
∂d∗
∂g
00
u (c0 )
= − u00 (c0 )+R
2 βu00 (c ) ∈ (−1, 0). The optimal d∗ is strictly decreasing with ω except in the region for
1
s
which small positive amounts of debt are dominated by zero debt as a result of the fixed cost of borrowing.
As resources continue to fall, d∗ may rise to the level of dmax
. For Group D, d∗ = dmax
= d¯ +
s
s
∗
∂s∗
0
∗ ∂s∗
ξ Ct (s∗ ) − g − EF C − d¯ ⇒ ∂d
∂g = ξ Ct (s ) ∂g − 1 , and because (2) holds, ∂g > 0 as was the case
for Group B. The conditions and properties of Groups E and F follow those of Groups A and B, respectively.
Derivation of the listed implications follows. Denote ωX as the highest value of in each Group X and
F (ω) the cumulative distribution function for ω, conditional on g and EF C. The monotonicity of the
policy implies that Group F has mass F (ωF ), Group E has mass F (ωE ) − F (ωF ), Group D has mass
F (ωD ) − F (ωE ), etc. Because the policy function is discontinuous, implications are shown for a discrete
change in the amount of grant aid received.
1. If the fixed cost γ > 0 then d > 0 and an increase in grant aid may lead to a greater than $1 for $1
21
reduction in loans for borrowers.
Consider a number δ ∈ (0, γ) and let s∗ (γ − δ) denote optimal schooling when d∗ = γ − δ. The choice
of d = 0 and s = s∗ (γ − δ) gives strictly greater utility than d = γ − δ and s = s∗ (γ − δ). This implies a
strictly dominated range of debt values between zero and some d > γ > 0. Now suppose all students have
ω = ωC and d = d. An increase in grant aid from g to g + δ/2 induces these students to stop borrowing.
Crowd-out is
4d
4g
=
δ
δ/2
= 2 > 1.
2. Grants only increase schooling for students facing some form of borrowing constraint.
This implication follows directly from the schooling policy functions.
3. Grants decrease educational attainment of students whose optimal debt level drops from (weakly) above
d to a positive amount below d.
Regardless of the choice of d, the choice of s satisfies (2):
C 0 (s) u0 (ω + EF C + g + d − C (s) − γ · κ0 )
= β (w0 (s) − ξκs (Rm − Rs ) Ct0 (s)) u0 w (s) − Rs d − κs (Rm − Rs ) d − d¯ − ξ Ct (s) − g − EF C − d¯
Label as s the value of s that satisfies this equation when d = d. As shown above, the choice of d = 0
dominates d ∈ (0, d). An increase in grants that induces switching from d = d to d = 0 decreases the value
of the left-hand side of the equation (because of the increase in grants and the fact that d ≥ γ) and increases
the value of the right-hand side. The necessary adjustment to s is downwards because (assuming d < dmax
s
to simplify notation):
∂
[C 0 (s) u0 (ω + EF C + g − C (s)) − β (w0 (s)) u0 (w (s) − Rs d)]
∂s
2
= C 00 (s) u0 (c0 ) − C 0 (s) 2 u00 (c0 ) − βw00 (s) u0 (c1 ) − βw0 (s) u00 (c1 )
>0
22